Learning Statistics with R - A tutorial for psychology students and other beginners, 2018a

Table 7.5: An illustration of two different ways of indexing a 2 ˆ 3 matrix. On the left we see the row
and column version, which is identical to the corresponding indexing scheme for a data frame of the same
size. On the right we see the single-index version, which is quite different to what we would get with a
data frame. The reason for this is that, for both data frames and matrices, the “row and column” version
exists to allow the human user to interact with the object in the psychologically meaningful way: since
both data frames and matrices are basically just tables of data, it’s the same in each case. However,
the single-index version is really a method for you to interact with the object in terms of its internal
structure, and the internals for data frames and matrices are quite different.
column
row 1 2 3
1 [1,1] [1,2] [1,3]
2 [2,1] [2,2] [2,3]
column
row 1 2 3
1 [1] [3] [5]
2 [2] [4] [6]
.......................................................................................................
(which can be qualitatively different to each other) and rows represent cases (which cannot). Matrices
are intended to be thought of in a different way. At a fundamental level, a matrix really is just one
variable: it just happens that this one variable is formatted into rows and columns. If you want a matrix
of numeric data, every single element in the matrix must be a number. If you want a matrix of character
strings, every single element in the matrix must be a character string. If you try to mix data of different
types together, then R will either spit out an error, or quietly coerce the underlying data into a list. If
you want to find out what class R secretly thinks the data within the matrix is, you need to do something
like this:
> class( M[1] )
[1] "numeric"
You can’t type class(M), because all that will happen is R will tell you that M is a matrix: we’re not
interested in the class of the matrix itself, we want to know what class the underlying data is assumed
to be. Anyway, to give you a sense of how R enforces this, let’s try to change one of the elements of our
numeric matrix into a character string:
> M[1,2] M
col.1 col.2 col.3
row.1 "2" "text" "1"
row.2 "5" "6" "7"
It looks as if R has coerced all of the data in our matrix into character strings. And in fact, if we now
typed in class(M[1]) we’d see that this is exactly what has happened. If you alter the contents of one
element in a matrix, R will change the underlying data type as necessary.
There’s only one more thing I want to talk about regarding matrices. The concept behind a matrix
is very much a mathematical one, and in mathematics a matrix is a most definitely a two-dimensional
object. However, when doing data analysis, we often have reasons to want to use higher dimensional
tables (e.g., sometimes you need to cross-tabulate three variables against each other). You can’t do this
with matrices, but you can do it with arrays. An array is just like a matrix, except it can have more
than two dimensions if you need it to. In fact, as far as R is concerned a matrix is just a special kind of
array, in much the same way that a data frame is a special kind of list. I don’t want to talk about arrays
too much, but I will very briefly show you an example of what a 3D array looks like. To that end, let’s
cross tabulate the speaker and utterance variables from the nightgarden.Rdata data file, but we’ll add
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